π-mesonic decay of the hypertriton

Abstract

The $\ensuremath{\pi}$-mesonic decay of the hypertriton is calculated based on a hypertriton wave function and 3$N$ scattering states, which are rigorous solutions of three-body Faddeev equations using realistic $\mathrm{NN}$ and hyperon-nucleon interactions. The total $\ensuremath{\pi}$-mesonic decay rate is found to be 101% of the free $\ensuremath{\Lambda}$ decay rate, which is close to the experimental data. Together with the nonmesonic decay the total lifetime of ${}_{\ensuremath{\Lambda}}^{3}$H is predicted to be 2.56 $\ifmmode\times\else\texttimes\fi{}$ 10${}^{\ensuremath{-}10}$ sec which is 3% smaller than for the free $\ensuremath{\Lambda}$ particle. The differential decay rate is evaluated as a function of the pion momentum. The decay into the $N+d+\ensuremath{\pi}$ channel is stronger than in the $3N+\ensuremath{\pi}$ channel in contrast to the situation for the nonmesonic decay. The ratio for the decay rate into ${}^{3}$He + ${\ensuremath{\pi}}^{\ensuremath{-}}$ to the decay rate into all channels including ${\ensuremath{\pi}}^{\ensuremath{-}}$ is found to be 0.379, which is close to the experimental value. We visualize the decay into the dominant channel $p+d+{\ensuremath{\pi}}^{\ensuremath{-}}$ in a Dalitz plot. Finally we compare the polarization of the outgoing proton in free unpolarized $\ensuremath{\Lambda}$ decay to the polarization of ${}^{3}$He in unpolarized ${}_{\ensuremath{\Lambda}}^{3}$H decay and we compare the closely related asymmetry of ${\ensuremath{\pi}}^{\ensuremath{-}}$ emitted parallel and antiparallel with respect to the spin direction for a polarized $\ensuremath{\Lambda}$ to the corresponding asymmetry for a polarized ${}_{\ensuremath{\Lambda}}^{3}$H.